Question

Let $A = 1,$ $B = 2,$ $C = 3,$ $\dots,$ $Z = 26. $ The product value of a word is equal to the product of the values of its letters. For example, CAB has a product value of $3 \times 1 \times 2 = 6. $ What common English word has a product value of $715$? It does not have to be of length $3$

Answer 1

make

Explanation:

Let's write out all letters and their values:

a1, b2, c3, d4, e5, f6, g7, h8, i9, j10, k11, l12, m13, n14, o15, p16, q17, r18, s19, t20, u21, v22, w23, x24, y25, z26

Now we find the prime factorization of 715.

715 = 5 × 11 × 13

That gives us the letters: e = 5, k = 11, m = 13

There is no word in English using only those three letters.

From our math studies, we remember the number 1, the multiplicative identity.

We can also use a = 1, since multiplying by 1 does not alter the product.

Letters: a, e, k, m

Word: make